Applied Algebra 2 – Section 8.5 Properties of Logarithms
Name
Using 𝐥𝐨𝐠 𝟓 𝟒 ≈ 𝟎. 𝟖𝟔𝟏 and 𝐥𝐨𝐠 𝟓 𝟗 ≈ 𝟏. 𝟑𝟔𝟓 to find the value of the expression to the nearest
thousandth. (3 decimal places)
1) log 5 36
4) log 5
1
4
3) log 5
5) log 5 324
6) log 5
Expand the expression. Assume all variables are positive.
7) log 2𝑥
8) log 𝑥 5
9) log 5 9𝑥 4
10) log 𝑥𝑦
11) log 4 𝑥 2 𝑦
12) log 3 7𝑥 3 𝑦 5
13) log
𝑥
𝑦
4
9
2) log 5 16
14) log
2
𝑥𝑦
𝑥2
15) log 7
3𝑦
16) log 3
𝑥
17) log 4 2
5𝑦
3𝑦 6
18) log 8 5
4𝑥
2𝑥
𝑦5
81
16
Condense the expression. Assume all variables are positive.
𝟏𝟗) log 3 + log 4
𝟐𝟎) log 4 9 + log 4 7
𝟏𝟗) log 2 − log 3
𝟐𝟎) 3 log 2 − log 4
𝟐𝟏) 2 log 5 + log 3
𝟐𝟐) 2log 8 − 2 log 4
𝟐𝟑) log 2 + log 𝑥
𝟐𝟒) log 𝑥 − log 2
𝟐𝟓) log 𝑥 + log 𝑦
𝟐𝟔) 3 log 𝑥 − 4 log 𝑦
𝟐𝟕) 5 log 𝑦 − log 𝑥
𝟐𝟖) 5 log 4 𝑥 + 8 log 4 𝑦
Condense the expression. Assume all variables are positive.
𝟐𝟗) log 3 + log 𝑥 − log 2
𝟑𝟎) 2 log 6 + 3 log 𝑥 − 4 log 𝑦 − 5 log 𝑧